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Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model

Pavel P. Popov1,*, Valentin Kasper1, Maciej Lewenstein1,2, Erez Zohar3, Paolo Stornati1, and Philipp Hauke4,5

  • *Contact author: pavel.popov@icfo.eu
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Phys. Rev. D 112, 014515 – Published 30 July, 2025

DOI: https://doi.org/10.1103/lpwm-65hr

Abstract

Gauge-field configurations with nontrivial topology have profound consequences for the physics of Abelian and non-Abelian gauge theories. Over time, arguments have been gathering for the existence of gauge-field configurations with fractional topological charge, called fractons. Ground-state properties of gauge theories can drastically change in presence of fractons in the path integral. However, understanding the origin of such fractons is usually restricted to semiclassical argumentation. Here, we show that fractons persist in strongly correlated many-body systems, using the multiflavor Schwinger model of quantum electrodynamics as a paradigm example. Through detailed numerical tensor-network analysis, we find strong fracton signatures even in highly discretized lattice models, at sizes that are implementable on already existing quantum-simulation devices. Our work sheds light on how the nontrivial topology of gauge theories persists in challenging nonperturbative regimes, and it shows a path forward to probing it in tabletop experiments.

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References (80)

  1. Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. I, Phys. Rev. 122, 345 (1961).
  2. D. Amati, K. Konishi, Y. Meurice, G. C. Rossi, and G. Veneziano, Nonperturbative aspects in supersymmetric gauge theories, Phys. Rep. 162, 169 (1988).
  3. A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Phys. Lett. 59B, 85 (1975).
  4. S. M. Barr, D. Chang, and G. Senjanović, Strong CP problem and parity, Phys. Rev. Lett. 67, 2765 (1991).
  5. C. Callan, R. Dashen, and D. Gross, The structure of the gauge theory vacuum, Phys. Lett. 63B, 334 (1976).
  6. G. ’t Hooft, Topology of the gauge condition and new confinement phases in nonAbelian gauge theories, Nucl. Phys. B190, 455 (1981).
  7. M. A. Shifman and A. V. Smilga, Fractons in the twisted multiflavor Schwinger model, Phys. Rev. D 50, 7659 (1994).
  8. E. Cohen and C. Gomez, Chiral symmetry breaking in supersymmetric Yang-Mills theory, Phys. Rev. Lett. 52, 237 (1984).
  9. N. Davies, T. J. Hollowood, V. V. Khoze, and M. P. Mattis, Gluino condensate and magnetic monopoles in supersymmetric gluodynamics, Nucl. Phys. B559, 123 (1999).
  10. H. Leutwyler and A. Smilga, Spectrum of Dirac operator and role of winding number in QCD, Phys. Rev. D 46, 5607 (1992).
  11. K. Melnikov and M. Weinstein, Lattice Schwinger model: Confinement, anomalies, chiral fermions, and all that, Phys. Rev. D 62, 094504 (2000).
  12. L. Funcke, K. Jansen, and S. Kühn, Topological vacuum structure of the Schwinger model with matrix product states, Phys. Rev. D 101, 054507 (2020).
  13. S. Kühn, J. I. Cirac, and M.-C. Bañuls, Quantum simulation of the Schwinger model: A study of feasibility, Phys. Rev. A 90, 042305 (2014).
  14. G. Magnifico, M. Dalmonte, P. Facchi, S. Pascazio, F. V. Pepe, and E. Ercolessi, Real time dynamics and confinement in the Zn Schwinger-Weyl lattice model for 1+1 QED, Quantum 4, 281 (2020).
  15. T. Chanda, J. Zakrzewski, M. Lewenstein, and L. Tagliacozzo, Confinement and lack of thermalization after quenches in the bosonic Schwinger model, Phys. Rev. Lett. 124, 180602 (2020).
  16. D. Banerjee and A. Sen, Quantum scars from zero modes in an Abelian lattice gauge theory on ladders, Phys. Rev. Lett. 126, 220601 (2021).
  17. J. C. Halimeh, L. Barbiero, P. Hauke, F. Grusdt, and A. Bohrdt, Robust quantum many-body scars in lattice gauge theories, Quantum 7, 1004 (2023).
  18. I. Sau, P. Stornati, D. Banerjee, and A. Sen, Sublattice scars and beyond in two-dimensional U(1) quantum link lattice gauge theories, Phys. Rev. D 109, 034519 (2024).
  19. J.-Y. Desaules, A. Hudomal, D. Banerjee, A. Sen, Z. Papić, and J. C. Halimeh, Prominent quantum many-body scars in a truncated Schwinger model, Phys. Rev. B 107, 205112 (2023).
  20. M. Brenes, M. Dalmonte, M. Heyl, and A. Scardicchio, Many-body localization dynamics from gauge invariance, Phys. Rev. Lett. 120, 030601 (2018).
  21. H. Lang, P. Hauke, J. Knolle, F. Grusdt, and J. C. Halimeh, Disorder-free localization with Stark gauge protection, Phys. Rev. B 106, 174305 (2022).
  22. T. V. Zache, N. Mueller, J. T. Schneider, F. Jendrzejewski, J. Berges, and P. Hauke, Dynamical topological transitions in the massive Schwinger model with a θ term, Phys. Rev. Lett. 122, 050403 (2019).
  23. N. Mueller, J. A. Carolan, A. Connelly, Z. Davoudi, E. F. Dumitrescu, and K. Yeter-Aydeniz, Quantum computation of dynamical quantum phase transitions and entanglement tomography in a lattice gauge theory, PRX Quantum 4, 030323 (2023).
  24. D. Pomarico, L. Cosmai, P. Facchi, C. Lupo, S. Pascazio, and F. V. Pepe, Dynamical quantum phase transitions of the Schwinger model: Real-time dynamics on IBM Quantum, Entropy 25, 608 (2023).
  25. T. Misumi, Y. Tanizaki, and M. Ünsal, Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multiflavor Schwinger model, J. High Energy Phys. 07 (2019) 018.
  26. M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, and T. Monz, A universal qudit quantum processor with trapped ions, Nat. Phys. 18, 1053 (2022).
  27. M. Meth, J. F. Haase, J. Zhang, C. Edmunds, L. Postler, A. Steiner, A. J. Jena, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. Muschik, and M. Ringbauer, Simulating 2D lattice gauge theories on a qudit quantum computer, arXiv:2310.12110.
  28. J. Schwinger, Gauge invariance and mass. II, Phys. Rev. 128, 2425 (1962).
  29. J. Schwinger, The theory of quantized fields. I, Phys. Rev. 82, 914 (1951).
  30. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  31. S. Chandrasekharan and U.-J. Wiese, Quantum link models: A discrete approach to gauge theories, Nucl. Phys. B492, 455 (1997).
  32. J. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  33. J. Struck, C. Ölschläger, M. Weinberg, P. Hauke, J. Simonet, A. Eckardt, M. Lewenstein, K. Sengstock, and P. Windpassinger, Tunable gauge potential for neutral and spinless particles in driven optical lattices, Phys. Rev. Lett. 108, 225304 (2012).
  34. F. Berruto, G. Grignani, G. W. Semenoff, and P. Sodano, Spectrum of the two-flavor Schwinger model from the Heisenberg spin chain, Phys. Rev. D 59, 034504 (1999).
  35. R. Dempsey, I. R. Klebanov, S. S. Pufu, and B. Zan, Discrete chiral symmetry and mass shift in the lattice Hamiltonian approach to the Schwinger model, Phys. Rev. Res. 4, 043133 (2022).
  36. E. Zohar, J. I. Cirac, and B. Reznik, Simulating compact quantum electrodynamics with ultracold atoms: Probing confinement and nonperturbative effects, Phys. Rev. Lett. 109, 125302 (2012).
  37. J.-Y. Desaules, E. J. Gustafson, A. C. Li, Z. Papić, and J. C. Halimeh, Robust finite-temperature many-body scarring on a quantum computer, arXiv:2309.11543.
  38. S. Chandrasekharan, Confinement, chiral symmetry breaking and continuum limits in quantum link models, Nucl. Phys. B, Proc. Suppl. 73, 739 (1999).
  39. U. Wiese, Ultracold quantum gases and lattice systems: Quantum simulation of lattice gauge theories, Ann. Phys. (Amsterdam) 525, 777 (2013).
  40. D. Banerjee, M. Bögli, M. Dalmonte, E. Rico, P. Stebler, U.-J. Wiese, and P. Zoller, Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories, Phys. Rev. Lett. 110, 125303 (2013).
  41. T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero, Real-time dynamics in u(1) lattice gauge theories with tensor networks, Phys. Rev. X 6, 011023 (2016).
  42. P. Zanardi, P. Giorda, and M. Cozzini, Information-theoretic differential geometry of quantum phase transitions, Phys. Rev. Lett. 99, 100603 (2007).
  43. S.-J. Gu, Fidelity approach to quantum phase transitions, Int. J. Mod. Phys. B 24, 4371 (2010).
  44. P. Hauke, F. M. Cucchietti, A. Müller-Hermes, M.-C. Bañuls, J. I. Cirac, and M. Lewenstein, Complete Devil’s staircase and crystal–superfluid transitions in a dipolar XXZ spin chain: A trapped ion quantum simulation, New J. Phys. 12, 113037 (2010).
  45. L. Wang, Y.-H. Liu, J. Imriška, P. N. Ma, and M. Troyer, Fidelity susceptibility made simple: A unified quantum Monte Carlo approach, Phys. Rev. X 5, 031007 (2015).
  46. M. C. Bañuls, K. Cichy, K. Jansen, and H. Saito, Chiral condensate in the Schwinger model with matrix product operators, Phys. Rev. D 93, 094512 (2016).
  47. M. Carena, H. Lamm, Y.-Y. Li, and W. Liu, Improved Hamiltonians for quantum simulations of gauge theories, Phys. Rev. Lett. 129, 051601 (2022).
  48. D. Spitz and J. Berges, Schwinger pair production and string breaking in non-Abelian gauge theory from real-time lattice improved Hamiltonians, Phys. Rev. D 99, 036020 (2019).
  49. E. Zohar, J. I. Cirac, and B. Reznik, Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices, Rep. Prog. Phys. 79, 014401 (2016).
  50. M. C. Bañuls et al., Simulating lattice gauge theories within quantum technologies, Eur. Phys. J. D 74, 165 (2020).
  51. M. Aidelsburger et al., Cold atoms meet lattice gauge theory, Phil. Trans. R. Soc. A 380, 20210064 (2021).
  52. S. Catterall, R. Harnik, V. E. Hubeny, C. W. Bauer, A. Berlin, Z. Davoudi, T. Faulkner, T. Hartman, M. Headrick, Y. F. Kahn et al., Report of the Snowmass 2021 Theory Frontier Topical Group on Quantum Information Science, (Fermi National Accelerator Laboratory (FNAL), Batavia, IL (USA); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (USA), 2022), 10.2172/1892238.
  53. T. S. Humble et al., Snowmass white paper: Quantum computing systems and software for high-energy physics research, in Snowmass 2021 (2022), arXiv:2203.07091.
  54. C. W. Bauer et al., Quantum simulation for high-energy physics, PRX Quantum 4, 027001 (2023).
  55. D. Beck et al., Quantum information science and technology for nuclear physics. Input into U.S. Long-Range Planning, 2023, arXiv:2303.00113.
  56. A. Di Meglio et al., Quantum computing for high-energy physics: State of the art and challenges, PRX Quantum 5, 037001 (2024).
  57. J. C. Halimeh, M. Aidelsburger, F. Grusdt, P. Hauke, and B. Yang, Cold-atom quantum simulators of gauge theories, arXiv:2310.12201.
  58. L. Funcke, T. Hartung, K. Jansen, S. Kühn, M.-O. Pleinert, S. Schuster, and J. von Zanthier, Exploring the phase structure of the multiflavor Schwinger model with quantum computing, arXiv:2211.13020.
  59. E. Zohar and J. I. Cirac, Removing staggered fermionic matter in U(N) and SU(N) lattice gauge theories, Phys. Rev. D 99, 114511 (2019).
  60. P. P. Popov, M. Meth, M. Lewestein, P. Hauke, M. Ringbauer, E. Zohar, and V. Kasper, Variational quantum simulation of U(1) lattice gauge theories with qudit systems, Phys. Rev. Res. 6, 013202 (2024).
  61. P. Jordan and E. P. Wigner, About the Pauli exclusion principle, Z. Phys. 47, 631 (1928).
  62. E. Zohar and J. I. Cirac, Eliminating fermionic matter fields in lattice gauge theories, Phys. Rev. B 98, 075119 (2018).
  63. X. Yuan, S. Endo, Q. Zhao, Y. Li, and S. C. Benjamin, Theory of variational quantum simulation, Quantum 3, 191 (2019).
  64. Quantum circuit library, https://github.com/wilkensJ/drawio-library (2023).
  65. N. Gomes, A. Mukherjee, F. Zhang, T. Iadecola, C. Wang, K. Ho, P. P. Orth, and Y. Yao, Adaptive variational quantum imaginary time evolution approach for ground state preparation, Adv. Quantum Technol. 4, 2100114 (2021).
  66. R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, Scalable circuits for preparing ground states on digital quantum computers: The Schwinger model vacuum on 100 qubits, PRX Quantum 5, 020315 (2024).
  67. A. Khan, B. K. Clark, and N. M. Tubman, Pre-optimizing variational quantum eigensolvers with tensor networks, arXiv:2310.12965.
  68. J. W. Mullinax, P. G. Anastasiou, J. Larson, S. E. Economou, and N. M. Tubman, Classical preoptimization approach for ADAPT-VQE: Maximizing the potential of high-performance computing resources to improve quantum simulation of chemical applications, J. Chem. Theory Comput. 21, 4006 (2025).
  69. R. D. Pisarski and F. Wilczek, Remarks on the chiral phase transition in chromodynamics, Phys. Rev. D 29, 338 (1984).
  70. Y. Aoki, G. Endrődi, Z. Fodor, S. D. Katz, and K. K. Szabő, The order of the quantum chromodynamics transition predicted by the standard model of particle physics, Nature (London) 443, 675 (2006).
  71. J. Wu, C. Li, Y. Wang, and T. Wumaier, Exploring the enigmatic chiral phase transition of QCD at finite temperature, arXiv:2401.17970.
  72. Z. Wang and S.-C. Zhang, Simplified topological invariants for interacting insulators, Phys. Rev. X 2, 031008 (2012).
  73. A. Elben, J. Yu, G. Zhu, M. Hafezi, F. Pollmann, P. Zoller, and B. Vermersch, Many-body topological invariants from randomized measurements in synthetic quantum matter, Sci. Adv. 6, eaaz3666 (2020).
  74. L. Lin, Y. Ke, and C. Lee, Topological invariants for interacting systems: From twisted boundary conditions to center-of-mass momentum, Phys. Rev. B 107, 125161 (2023).
  75. P. P. Popov, V. Kasper, M. Lewenstein, E. Zohar, P. Stornati, and P. Hauke, Nonperturbative signatures of fractons in the twisted multiflavor Schwinger model, 10.5281/zenodo.15495458 (2025).
  76. S. R. Coleman, There are no Goldstone bosons in two-dimensions, Commun. Math. Phys. 31, 259 (1973).
  77. P. Weinberg and M. Bukov, quspin: A python package for dynamics and exact diagonalisation of quantum many body systems. Part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  78. M. Fishman, S. R. White, and E. M. Stoudenmire, The itensor software library for tensor network calculations, SciPost Phys. Codebases, p. 410.21468/SciPostPhysCodeb.4 (2022).
  79. W.-L. You and L. He, Generalized fidelity susceptibility at phase transitions, J. Phys. Condens. Matter 27, 205601 (2015).
  80. G. Sun, A. K. Kolezhuk, and T. Vekua, Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions, Phys. Rev. B 91, 014418 (2015).

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Phys. Rev. D 112, 014515– Published 30 July, 2025
  • Received 20 August 2024
  • Accepted 18 June 2025
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